Consider a quadratic equation $$ax^2 + bx + c = 0$$, where $$2a + 3b + 6c = 0$$ and let $$g(x) = a\frac{x^3}{3} + b\frac{x^2}{2} + cx$$. Statement 1: The quadratic equation has at least one root in the interval $$(0,1)$$. Statement 2: The Rolle's theorem is applicable to function $$g(x)$$ on the interval $$[0,1]$$.

A

Statement 1 is false, Statement 2 is true.

B

Statement 1 is true, Statement 2 is false.

C

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

D

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.